Almost 50 years ago Jocelyn Bell built a new telescope with her supervisor Antony Hewish that had an unusual property: it had high time resolution. The radio sky was thought to only change on long timescales but this new telescope's ability to explore a different regime of phase space meant that it made one of the greatest discoveries in astronomy, that of pulsars. Pulsars are neutron stars, the collapsed cores of once-massive stars. They have been used to perform some of the most accurate experiments in physics, and were the motivation for the construction of the LIGO telescope that recently discovered gravitational waves. In this talk Professor Matthew Bailes will explain how whilst trying to find new pulsars astronomers stumbled across a brand new phenomenon, the Fast Radio Bursts. These millisecond-duration radio flashes appear to be coming from half way across the Universe but nobody knows what they are. Presented on 30 September 2016.